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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: **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 (x_{1}, y_{1}) is (1,2).

The points (x_{2}, y_{2}) 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 = y_{2}-y_{1} /x_{2}-x_{1}

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 = 0 ——- (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:** 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.