Question

Find the slope and y-intercept of the line given below
$y=3x-5$
A. -3,5
B. 3/5,1
C. 3,5
D. 3,-5

Answer 1

First we recall the slope-intercept form of a line, which is given by $y=mx+c$.
Where, $m=$ slope of a line
$c=$ $y$- intercept of the line
When we compare the coefficients of the equation given in the question with this standard form, we get the slope of the line. To get $y$- intercept of the line we put the value of $x=0$ in the given equation.

Complete step-by-step answer:
We have given that the equation of line $y=3x-5$
We have to find the slope and $y$- intercept of the line.
We know that slope is a line defined as the change in $y$- coordinates with respect to change in $x$- coordinates.
To find the slope of a line, we compare the given equation with the slope-intercept form of a line.
$y=mx+c$ Where, $m=$ slope of a line
When we compare the coefficient of $x$, we get $m=3$
So, the slope of a line $y=3x-5$ is $3$.
As we know that an intercept is the point of intersection of the line with the coordinate axes.
As we know that to find the $y$- intercept of the line, the value of $x$ should be taken as zero in the equation of the line. Then, the equation of the line becomes
$\begin{aligned} & y=3\times 0-5 \\\ & y=-5 \\\ \end{aligned}$
So, the $y$- intercept of the line $y=3x-5$ is $-5$.
Option D is the correct answer.

Note: The possibility of a mistake can be in comparing the coefficients of the given equation with the standard equation. When we compare the coefficients we have to compare the value with a sign. If the coefficient of $x$ has negative value then, the slope of the line will be negative. To find the $x$- intercept of the line, the value of $y$ should be taken as zero in the equation of the line and vice-versa.