Question

How do you write an equation of a line with slope $4$ and y intercept $-6$ ?

Answer 1

From the question given a line has a slope of $4$ and it has a y intercept is $-6$, we have to find the equation of the line. As we know that the slope intercept form that is if a line has a slope “m” and it has an intercept “c” then the equation of the line is $\Rightarrow y=mx+c$ this equation is known as slope-intercept form. From this equation we will get the required equation of line.

Complete step by step solution:
From the question given the equation of a line has a slope, that is the slope “m” is
$\Rightarrow m=4$
And also given that the line has a y intercept, that is the y intercept “c” is
$\Rightarrow c=-6$
As we know that the slope intercept form that is if a line has a slope “m” and it has a intercept “c” then the equation of the line is
$\Rightarrow y=mx+c$
By comparing here, we will get,
$\Rightarrow m=4$
$\Rightarrow c=-6$
Now by substituting the above values in their respective position in the formula of slope-intercept form we will get the required equation of line,
$\Rightarrow y=\left( 4 \right)x-6$
By simplifying further, we will get,
$\Rightarrow 4x-y-6=0$
Therefore, this is the required line equation which has a slope of $4$ and y-intercept of $-6$.
The figure will be as follows.

Note: Students must be very careful in doing the calculations. Students should recall all the formulas and line equations of the co-ordinate geometry, while solving the above question.
Students should know the slope intercept form which is $y=mx+c$ to solve the question.