Worksheet on Slope-Intercept Form is given with various questions and hidden answers. Get the various examples on the slope-intercept form in our 10th Grade Math Worksheet. All the students can easily be aware of the tips to solve different kinds of problems on slope intercept form here. Practice using our slope-intercept form worksheet and clear all your doubts in no time. Use this best opportunity to learn slope intercept form concept of math in an easy way by referring to our page.
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Slope Intercept Form Worksheet with Answers PDF
Problem 1: Find the equation of a straight line whose y-intercept is (0,-4) and the slope is 5 by using the slope-intercept form?
Solution:
As given in the question,
The slope of a line m is 5.
The y-intercept of a line is (0,-4) which is the value of c is -4.
Now, we will find the equation of the given line.
Using the slope-intercept formula, the equation of the given line is,
y = mx +c
Now, substitute the given values in the formula. Then we get,
y = (5) x – 4
y=5x-4
5x-y-4 = 0
So, the equation of the given line is, y =5x-4 or 5x-y-4=0.
Problem 2:Â Find the straight line equation with slope m = 4 and which passes through the point (-3, -6).
Solution:
As given in the question,
The slope of a line m is 4.
The points x-coordinate and y-coordinates are -3 and -6.
By using the slope-intercept form, we will find the equation of a line.
The slope-intercept formula is, y = mx+c
Now, place the given values in the above equation. We get,
-6 = 4(-3) + c
-6 = -12+c
c = -12 + 6 = -6
Hence, the required equation will be y= 4x-6.
Problem 3: Find the equation of the lines for which tan θ = 1/2, where θ is the inclination of the line such that:
(i) y-intercept is -7
(ii) x-intercept is 5/2
Solution:
As given in the question,
The slope of a line is tan θ i.e., m= tanθ =1/2.
The following are the values, we will find
(i) The y-intercept value is, c = -7
The formula for the Equation of the line using the slope-intercept form is,
y = mx + c
Now, put the values in a formula.
The equation is y = (1/2)x + (-7)
In another form, the equation will be,
2y = x – 14
x – 2y – 14 = 0
Thus, the required equation of a line is x – 2y – 14 = 0.
(ii) The x-intercept is d = 5/2
We know, the equation of slope intercept form with x-intercept is,
y = m(x – d)
Placing the values in the equation. It will be,
y = (1/2)[x – (5/2)]
i.e., 2y = (2x – 5)/2
2y*2 = 2x – 5
2x – 4y – 5 = 0
So, the required equation of a line is y = (1/2)[x – (5/2)] or 2x – 4y – 5 = 0.
Problem 4: Using the slope-intercept, find the equation of the horizontal line that intersects the y-axis at (0,9)?
Solution:
In the given question,
The y-intercept of the line is (0, b) = (0,3) that means b = 9.
The line is horizontal, so its slope is m = 0.
Now, we will find the equation of the given line.
By using the slope-intercept formula, the equation of the given line is,
y = mx + b
Substitute the given values in the above equation. Then,
The value is y = (0)x + 9
y = 9
So, the equation of the given line is y = 9.
Problem 5: What is the equation of a line which is parallel to the line is y= 12x-5 and whose y-intercept is (2/3)
Solution:
As per the given information,
The y-intercept of the line is b = 2/3.
The equation of a line is y = 12x-5.
We will find the equation which is parallel to the given line.
The formula for slope-intercept form is y = mx + b.
Based on the given equation, the slope of a line m is 12.
The given line is parallel to the required line, so their slopes are equal.
Then the slope of the required line is also, m = 3
Now, substitute the values in the slope-intercept formula.
y = 12x+(2/3).
Hence, the equation of the required line is y = 12x +2/3.
Problem 6: The equation of a line in slope-intercept is 3x=5y-12. To determine the slope and y-intercept?
Solution:
As given in the question,
The equation of a line in slope-intercept form is 3x=5y-12.
Now, we will find the slope and y-intercept using the given equation.
First, rewrite the given equation. It is in the form of y=mx+c.
The equation is 5y= 3x+12.
y = (3/5)x + 12/5
Then the value of the slope of a line is m =3/5 and the y-intercept value is b=12/5.
Therefore, based on the given equation of a line, the values of m and b are 3/5 and 12/5.
Problem 7: Using the slope-intercept form, write an equation of the line which is passing through the points (1,3) and (4,2)?
Solution:
As per the given information,
The points on the x-coordinate and y-coordinate are (x1, y1) is (1,2).
The points (x2, y2) are (4, 3).
We will find out the equation of a line in slope-intercept form.
Here, the line passes through two points values. So, first, find the value of the slope of a line.
We all know that the formula for the slope of a line is,
m = y2-y1 /x2-x1
Place the points values in the above formula, then the slope is,
m = 3-2/4-1 = 1/3
m= 1/3.
By using the slope value and the point (1,2) to find the y-intercept.
The formula for the slope-intercept form of an equation is, y = mx+ b.
Substitute the values in the slope-intercept form. It will be,
2 = (1/3)(1)+b
2=1/3+b
2*3 = 1+b
6-1 =b
b=5.
Now, write the equation in a slope-intercept form as,
y =mx+b
y = (1/3)x+5
Hence, the equation of a line is y = (1/3)x+5.
Problem 8: Find the equation of the line that passes through the points (8,6) and has an x-intercept at x=−2?
Solution:
As given in the question,
The points on the x-coordinate and y-coordinate are (x1, y1) is (8,6).
The points (x2, y2) are (-2, 0).
Now, we will find out the equation of a line in slope-intercept form.
The line passes through the two points. So, first, find the value of the slope of a line.
The formula for the slope of a line is,
m = y2-y1 /x2-x1
substitute the points values in the above formula, then the slope is,
m = 0-6/-2-8 = -6/-10
m= 3/5.
Using the slope of a line value and the point (8,6) to find the y-intercept.
The formula for the slope-intercept form of an equation is, y = mx+ b.
Substitute the values in the slope-intercept form. It will be,
6 = (3/5)(8)+b
6*5=3(8)+b
30 = 24 +b
30-24 =b
b=6.
Now, write the equation in a slope-intercept form as,
y =mx+b
y = (3/5)x+6
Hence, the required equation of a line is y = (3/5)x+6.
Problem 9: The A and B are two points on the x-axis. A is on the positive side of the x-axis at a distance of 5 and B is on the negative side at the distance of 3 from the origin O. P is the midpoint of AB. What is the equation of the line PC which cuts an intercepts 2 on the y axis and also finds the slope of a line of PC?
Solution:
Given that, on the x-axis, A and B are two points.
On the x-axis, the positive side distance is 5, and the x-axis negative side distance is 3.
P is the midpoint of AB. So, the intercept is c = 5-3 =2.
In both coordinates, the Y will be zero.
The formula for slope-intercept form is,
Y=mx+c
Now, substitute the values in the above formula. It will be,
0 = m(5)+2
0=5m+2
5m= -2
m=-2/5.
Now, using the value of x as 3. Then the equation is,
The intercept c = 3-5 = -2.
0 = m(3)+(-2)
0 = 3m -2
3m =2
m = 2/3
Next, find the slope-intercept form. The formula is,
Y = mx+c
Substitute the value in above equation. It will be,
y = (-2/5)x+ 2
y-2 = (-2/5)x
5(y-2) = -2x
5y-10 = -2x
5y-2x-10 = 0Â ——- (1)
Now, substitute the another slope value i.e., 2/3.
Y = (2/3)x+2
y-2 = (2/3)x
3(y-2) = 2x
3y – 6 =2x
3y-2x-6 = 0 ——-(2)
Equate equation (1) & (2)
5y -2x-10 = 3y-2x-6
5y-3y+2x+2x-10+6 = 0
2y+4x-4=0
2(y+2x) =4
y+2x = 4/2
The equation of a line is y+2x =2.
According to the slope-intercept form formula, y = mx+c
So, the equation is re-write is,
y = -2x+(4/2)
So, the slope of a line is -2 and the equation of a line is 2x+y = 2.
Problem 10:Â Find the equation of a straight line whose y-intercept is (0,3) and the slope is 2 by using the slope-intercept form?
Solution:
As given in the question,
The value of the slope of a line m is 2.
The y-intercept of a line is (0,3) which is the value of c is 3.
Now, we will find the equation of the given line.
The equation of the given line using the slope-intercept form formula is,
y = mx +c
Now, substitute the given values in the formula. Then we get,
y = (2)x+3
y=2x+3
2x-y-3 = 0
So, the equation of the given line is, y =2x+3 or 2x-y-3=0.