Q18. - Algebra 2

Question

State the slope and y-intercept of the graph of each equation.

$\mathbf{cx}+\mathbf{y}=\mathbf{d}$

Step-by-Step Solution

Answer

The slope of the given line is $-c$ and the y-intercept of the given line is $d$.

Step 1 – State the concept

The general equation of a straight line in slope-intercept form is given as $y=mx+c$, where $m$ is the slope and $c$ is the y-intercept.

Step 2 – List the given data

The given equation of the line is $cx+y=d$.

Step 3 – Identify the slope and intercept

Convert the given equation to slope-intercept 

form as follows:

 

$cx+y=d$   (Given equation)

 

$cx+y-cx=d-cx$  (Subtract $cx$ from both sides)

 

$y=d-cx$  (Simplify)

 

$y=-cx+d$  (Rearrange)

 

So, the given equation in slope-intercept form is $y=-cx+d$.

 

Comparing the obtained equation, 

$y=-cx+d$ with $y=mx+c$, $m=-c$ and $c=d$.

 

This implies that the slope of the given line is $-c$ and the y-intercept of the given line is $d$.