
How do you graph using slope and intercept of ?
Answer
463.5k+ views
Hint: In this question we have to plot a graph using slope and intercept of a given straight line. Firstly, we will convert the given equation into a slope intercept form of a straight line. It can be done by first subtracting from both sides of the given equation. Then dividing each term by 2 and rearranging the obtained equation. We then compare the given equation of a line with the standard slope intercept form of a line and find the slope and intercept. We substitute different values of x and obtain the values of y. Then we plot the points in the x-y plane and we will have a required graph of the given equation.
Complete step by step answer:
Given the equation of a straight line …… (1)
We are asked to draw the graph using the slope and intercept of the given line.
So firstly we will try to find out the slope of a line given in the equation (1).
To find this, we need to convert our given equation into slope intercept form of a straight line.
The general equation of a straight line in slope intercept form is given by,
…… (2)
where is the slope or gradient of a line and is the intercept of a line.
Now we convert the given equation of a line into slop intercept form by rearranging the terms.
Consider the equation of a line given in the equation (1).
Subtracting from both sides of the equation (1), we get,
Combining the like terms we get,
Now dividing throughout by 2 we get,
Rearranging the above equation we get,
…… (3)
Comparing with the standard slope intercept form given in the equation (2), we get,
and .
Now to draw a graph of a linear equation, we first assume some values for the variable x and substitute in the above equation and obtain the values of the other variable y.
Then plotting these values of x and y on the x-y plane, we get the graph of the given equation.
We first let different values of x.
Substituting in the equation (3), we have,
Substituting in the equation (3), we have,
Substituting in the equation (3), we have,
Substituting in the equation (3), we have,
Note: Graph of a linear equation is always a straight line. Remember the general form of an equation of a straight line given by , where m is the slope of the line and c is the intercept. If while calculating the points, if someone has made a mistake then all the points obtained after calculations will not come on a straight line. So, we need to calculate carefully while doing calculations for points and also while plotting in x-y plane.
Complete step by step answer:
Given the equation of a straight line
We are asked to draw the graph using the slope and intercept of the given line.
So firstly we will try to find out the slope of a line given in the equation (1).
To find this, we need to convert our given equation into slope intercept form of a straight line.
The general equation of a straight line in slope intercept form is given by,
where
Now we convert the given equation of a line into slop intercept form by rearranging the terms.
Consider the equation of a line given in the equation (1).
Subtracting
Combining the like terms we get,
Now dividing throughout by 2 we get,
Rearranging the above equation we get,
Comparing with the standard slope intercept form given in the equation (2), we get,
Now to draw a graph of a linear equation, we first assume some values for the variable x and substitute in the above equation and obtain the values of the other variable y.
Then plotting these values of x and y on the x-y plane, we get the graph of the given equation.
We first let different values of x.
Substituting
Substituting
Substituting
Substituting
x | 0 | 1 | 2 | 3 |
y | 10.5 | 9 | 7.5 | 6 |

Note: Graph of a linear equation is always a straight line. Remember the general form of an equation of a straight line given by
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