Question

How do you find the slope and intercepts to the graph y=2x-3?

Answer 1

This type of question is based on the concept of equation of lines. We are given the equation of line is y=2x-3. We know that the slope-intercept form of the equation of line is y=mx+c, where m is the slope of the line and c is the y-intercept of the line. On comparing the slope intercept form of the line with the given line, we get m=2 and c=-3. Thus, we get that the slope of the equation is 2 and the y-intercept is -3. Now, we have to find the x-intercept by substituting y=0 in the given equation. Add 3 on both the sides of the equation and divide the whole expression by 2 to find the x-intercept.

Complete step by step solution:
According to the question, we are asked to find the slope and intercept of the line equation y=2x-3.
We have been given the equation of line is y=2x-3. ------------(1)
Let us first plot the graph for y=2x-3.

We know that the slope intercept form of the equation is y=mx+c, where m is the slope of the line and c is the y-intercept of the equation, that is the line crosses the y-axis at (0,c).
Let us now compare the slope intercept equation with the given equation.
We find that the coefficient of x in equation (1) is 2 which is the slope of the equation.
Therefore, we get m=2.
Now, we have to find the intercept of the equation.
We know that the constant c in the slope intercept form is the y-intercept.
Here, from equation (1), we get that the constant is -3.
That is, the y-intercept of the line is equal to -3.
Therefore, we get c=-3. And the y intercept is at (0,-3).
Now, we have to find the x-intercept.
To find the x-intercept, we have to substitute the value of y as 0.
$\Rightarrow 2x-3=0$
Add 3 on both the sides of the equation.
$\Rightarrow 2x-3+3=0+3$
On further simplifications, we get
2x=3
Divide the expression by 2.
$\Rightarrow \dfrac{2x}{2}=\dfrac{3}{2}$
We find that 2 are common in both the numerator and denominator of the LHS. On cancelling 2, we get
$x=\dfrac{3}{2}$
Therefore, we get that the x-intercept is at $\left( \dfrac{3}{2},0 \right)$
Therefore, the slope of the line y=2x-3 is 2 and the x and y intercepts are at $\left( \dfrac{3}{2},0 \right)$ and (0,-3) respectively.

Note:
Whenever we get such types of problems, we have to make certain calculations and convert the given equation to the form y=mx+c. This will help us to reduce the number of steps to find the answer. We should find the intercepts of x and y separately since it is mentioned in the question. We can verify the obtained intercepts by comparing the points with the graph obtained.