find expressions for the slope and x- and y-intercept for ax+by=c where a b and c are nonzero integer

the x intercept is when y=0, in this case ax=c =>x=c/a
the y intercept is when x=0, in this case by=c =>y=c/b
the slope: by=-ax+c =>y=(-a/b)x+(c/b), so the slope is -a/b, the y intercept is c/b, which matches the answer in the second line.

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MrRoyal MrRoyal · Answer 2 · 2021-10-22T11:32:11+02:00

The equation represents a linear function.

The x-intercept is: [tex]\mathbf{x = \frac ca}[/tex]
The y-intercept is: [tex]\mathbf{y = \frac cb}[/tex]
The slope is : [tex]\mathbf{Slope = - \frac ab }[/tex]

The equation is given as:

[tex]\mathbf{a x + b y = c}[/tex]

Set y to 0, to calculate the x-intercept

[tex]\mathbf{ax + b \times 0 = c}[/tex]

[tex]\mathbf{ax = c}[/tex]

Divide by a

[tex]\mathbf{x = \frac ca}[/tex]

Hence, the x-intercept is: [tex]\mathbf{x = \frac ca}[/tex]

Set x to 0, to calculate the y-intercept

[tex]\mathbf{a\times 0 + b y= c}[/tex]

[tex]\mathbf{by = c}[/tex]

Divide by b

[tex]\mathbf{y = \frac cb}[/tex]

Hence, the y-intercept is: [tex]\mathbf{y = \frac cb}[/tex]

Recall that: [tex]\mathbf{a x + b y = c}[/tex]

Subtract ax from both sides

[tex]\mathbf{by = - ax+c }[/tex]

Divide both sides b

[tex]\mathbf{y = - \frac ab x+\frac bc }[/tex]

The slope of the equation is the coefficient of x

Hence, the slope is : [tex]\mathbf{Slope = - \frac ab }[/tex]

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