Question

How do you find the x and y intercept of $y=-\dfrac{3}{4}x+4$?

Answer 1

To solve above question we will use the concept of coordinate- geometry. We will also use the concept that x-intercept is the point at which the line cuts the x-axis and y-intercept is the point at which the line cuts the y-axis.

Complete step by step answer:
We can see that we are given a line equation in the question. So, we will use the concepts of the coordinate geometry to find the x and y intercept of the line.
We know that the x-intercept of a line is the point at which the line cuts the x-axis and y-intercept of the line is the point at which line cuts the y-axis.
Also, we know that x-intercept of the line is obtained by putting y = 0 in the given line equation $y=-\dfrac{3}{4}x+4$ and y-intercept of the line is obtained by putting x = 0 in the given line equation $y=-\dfrac{3}{4}x+4$.
So, when we put x = 0, we will get:
$\Rightarrow y=-\dfrac{3}{4}\left( 0 \right)+4$
$\therefore y=4$
Hence, y-intercept is equal to 4.
Now, when we put y = 0 we will get:
$\Rightarrow 0=-\dfrac{3}{4}x+4$
$\Rightarrow \dfrac{3}{4}x=4$
$\therefore x=\dfrac{16}{3}$

Hence, x-intercept is equal to $\dfrac{16}{3}$.

Note: Students are required to note that the general equation of the line in slope-intercept form is given as y = mx + c, where m is the slope of the line and c is the y-intercept of the line given. Also, the general equation of the line whose two points are $\left( {{x}_{1}},{{y}_{1}} \right),\left( {{x}_{2}},{{y}_{2}} \right)$ is given by $\left( y-{{y}_{1}} \right)=\dfrac{\left( {{y}_{2}}-{{y}_{1}} \right)}{\left( {{x}_{2}}-{{x}_{1}} \right)}\left( x-{{x}_{1}} \right)$ . Also, students are required to memorize the above described condition for finding x and y intercept.