To determine the x- and y-intercepts is best to write the equation in slope-intercept form.
Given
[tex]8x-12y=-24[/tex]-Pass the x-term to the right side of the equation by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 8x-8x-12y=-8x-24 \\ -12y=-8x-24 \end{gathered}[/tex]-Divide both sides of the equal sign by -12
[tex]\begin{gathered} \frac{-12y}{-12}=\frac{-8x}{-12}-\frac{24}{-12} \\ y=\frac{2}{3}x+2 \end{gathered}[/tex]So the equation in slope-intercept form is:
[tex]y=\frac{2}{3}x+2[/tex]a) The x-intercept is the point where the line crosses the x-axis, at this point, the y-coordinate is equal to zero. To determine the x-coordinate of the intercept, you have to equal the equation to zero and calculate the corresponding value of x:
[tex]0=\frac{2}{3}x+2[/tex]-Subtract 2 to both sides of the equal sign
[tex]\begin{gathered} 0-2=\frac{2}{3}x+2-2 \\ -2=\frac{2}{3}x \end{gathered}[/tex]-Multiply both sides of the expression with the reciprocal fraction of 2/3
[tex]\begin{gathered} (-2)\frac{3}{2}=(\frac{2}{3}\cdot\frac{3}{2})x \\ -3=x \end{gathered}[/tex]The x-intercept is (-3,0)
b) The y-intercept is the point where the line crosses the y-axis, at this point, the x-coordinate is equal to zero. To determine the y-intercept, replace the equation with x=0 and calculate the corresponding value of y:
[tex]\begin{gathered} y=\frac{2}{3}x+2 \\ y=\frac{2}{3}\cdot0+2 \\ y=2 \end{gathered}[/tex]The y-intercept is (0,2)
c) To graph the line, plot both intercepts on the coordinate system and then link both points with a line:
