Take the help of the Worksheet on Slope and Intercepts solutions while preparing to find the slopes and intercepts. It is helpful for the students who are willing to solve the problems based on the equation of a straight Line Slope and Intercepts. We have covered various types of questions in our Finding the Slope and Intercept Problems in our Worksheet. Let us see the various problems we have given on the worksheet and prepare well for the exam.
Check out 10th Grade Math Concepts and worksheets for free of cost on our website. We have given very simple ways to solve slope and intercept problems. Therefore, follow the step-by-step procedure to make your practice better and easy.
Also, Read:
Finding Slope and Intercepts Worksheet with Answers PDF
Below are the different slope and intercept finding problems. Check how to find intercepts using the equation of a line and how to find slope using two points.
Problem 1: Find the slope and intercepts on the y-axis of the following equations of a straight line?
(i) The equation of a line is x – 4y – 3 = 0
(ii) 3x+6y+8 =0
Solution:
As given in the question, the equations of a straight line are given.
Now, we will find the value of the slope of a line and the y-intercept value.
The following are,
(i) The equation of a line is x-4y-3 =0.
It can be rewritten as, 4y = x-3
y= (1/4)x + (-3/4)
It is in the form of y = mx+b
So, the slope of a line m is 1/4, and the y-intercept value b = -3/4
(ii) The equation of a straight line is 3x+6y+8=0
Now, find its slope and the y-intercepts.
The equation is rewritten as,
6y = -3x-8
y = (-3/6)x +(-8/6)
The above equation is in the form of y = mx+b
Comparing the formula with the equation is,
The slope m = (-3/6)
The y-intercept is (-8/6)
Therefore, the given equation of a line slope is (-1/2) and the y-intercept b is (-8/6).
Problem 2: The following are the equations of a line, using this find the Slope of a line and the y-intercept value?
(i) y-7 =0
(ii) x√3 + y/2 = 1
Solution:
The equations of a line are given in a question.
To find out the slope and the y-intercept of a line.
The following are,
(i) The equation of a line is y-7 =0.
It can be rewritten as, y=7
y= (0)x + 7
It is in the form of y = mx+b
So, the slope of a line m is 0, and the y-intercept value b = 7
(ii) The equation of a straight line is x√3 + y/2 = 1
Now, find its slope and the y-intercepts.
The equation is rewrite as,
x√3 + y/2 = 1
x/3+y/2 = 1
(2x+3y)/6 = 1
2x+3y = 6
3y = -2x+6
y = (-2/3)x + 2
The above equation is in the form of y = mx+b
Comparing the above formula with the equation. Then, we get
The slope pf a line m = (-2/3)
The y-intercept of a line is 2.
Hence, the given equation of a line slope is (-2/3) and the y-intercept b is 2.
Problem 3: Find the slope and y-intercept of a line, where the equation is y =4?
Solution:
Given that,
The equation is y =4.
Now, find out the slope and y-intercept.
Comparing the given equation with y=mx+c. We get,
y = (0)x+4
From the above equation, slope = 0, and y-intercept is 4.
Therefore, the slope and intercept are 0 and 4.
Problem 4: The equation of the line is x+5y-9=0 in slope intercept form and then find the slope and the y-intercept of the line?
Solution:
In the given question, the equation of a line is x+5y-9 =0.
Now, we will find the slope of a line and the y-intercept value.
The equation is rewrite as, 5y = -x+9
y = (-1/5)x+9
The above equation looks like a slope-intercept form formula i.e., y =mx+c
Based on the formula, the slope of a line is m =(-1/5), and the intercept value is 9.
Thus, the values of the slope of a line and y-intercept are -1/5 and 9.
Problem 5: What is the inclination of a line whose slope is 1?
Solution:
As per the given information,
The slope of a line is 1.
Now, we need to find out the inclination of the line.
We know that θ is the inclination of the line with the x-axis.
The value of tan 45° = 1.
So, the slope value is 1, which means m = tan 45° = 1.
The θ = 45°.
Hence, the inclination of a line is 45°.
Problem 6: Find the value of inclination of a line whose slope of a line is √3?
Solution:
As per the given information,
The slope of a line is m = √3.
Now, we need to find out the inclination of the line. Where θ is the inclination of the line with the x-axis.
So, the tan θ = √3.
We know that m = tan 60° = √3.
Therefore θ = 60°.
Hence, using the slope value the inclination of a line is 60°.
Problem 7: The straight lines are joined by two points (1,0) and (4,3). Find the slope and inclinations of the straight line?
Solution:
In the given question,
The points on the x-coordinate and y-coordinate are (x1, y1) is (3,0).
The points (x2, y2) are (4, 6).
We will find out the equation of a line in slope and inclination of a line.
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 = 6-3/4-1 = 3/3
m= 3/3 = 1.
Now, we will find the inclination of a line value.
The slope m = tan θ = 1
We know that tan 45° = 1.
So, the θ is the inclination of the line.
Hence, the straight line inclination is θ = 45°, and the slope of a line is 1.
Problem 8: What is the slope of a line whose inclination is 135°?
Solution:
As given in the question,
The inclination of a line is θ = 135°.
Now, we will find the slope of a line using the inclination value.
The slope of a line is m = tan θ
where, θ = 135°. Substitute this θ value in the above equation.
Then the slope is, m = tan θ = tan 135° = -1.
Thus, the slope of a line m is -1.
Problem 9: Find the slope and inclination of the straight lines joined by two points (4,6) and (-2,6)?
Solution:
In the given question,
The points on the x-coordinate and y-coordinate are (x1, y1) is (4,6).
The points (x2, y2) are (-2, 6).
We will find out the equation of a line in slope and inclination of a line.
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 = 6-6/-2-4 = 0/-6
m= 0/-6 = 0.
Now, we will find the inclination of a line value.
The slope m = tan θ = 0
We know that tan 0° = 0.
where the θ is the inclination of the line.
Therefore, the given straight line inclination is θ = 0°, and the slope is 0.
Problem 10:Â Find the intercept of the straight lines on the coordinate axes. The equation of a line is 6x + 8y=12?
Solution:
Given that, the equation of a line is 6x + 8y = 12.
Now, we will find the x-intercept and y-intercept values.
We know that the intercept is x/a + y/b = 1. So, the x-intercept is a and b is the y-intercept.
The equation is 6x + 2y = 12, it can be
2x+6y/12 = 12/12
2x/12 + 6y/12 = 1
x/6 + y/2 = 1
So, x intercept = 6 and the y-intercept = 2.
Therefore, the given straight line x-intrecept and the y-intercept is 6 and 2.