Question

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

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

Short answer

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

Step-by-step solution

– 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.

– List the given data

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

– 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 $d$.