SOLUTION
Given the question in the image, the following are the solution steps to get the intercepts of the equation
Step 1: Write the given equation
[tex]-7x-3y=42[/tex]Step 2: Write the equation in form of a slope-intercept form by making y the subject of the formula
[tex]\begin{gathered} -7x-3y=42 \\ -3y=42+7x \\ \text{divide both sides by -3} \\ y=-\frac{42+7x}{3} \\ y=-(\frac{42}{3}+\frac{7x}{3}) \\ y=-(14+\frac{7x}{3}) \\ y=-\frac{7}{3}x-14 \end{gathered}[/tex]Step 3: Find the x-intercept
The x-intercepts are points where the graph of a function or an equation crosses or “touches” the x-axis of the Cartesian Plane. You may think of this as a point with y-value of zero.
To find the x-intercepts of an equation, let y = 0, then solve for x
[tex]\begin{gathered} y=-\frac{7}{3}x-14 \\ \text{set y=0} \\ 0=-\frac{7}{3}x-14 \\ \frac{7}{3}x=-14 \\ \text{multiply both sides by inverse of 7/3} \\ \frac{7}{3}x\times\frac{3}{7}=-14\times\frac{3}{7} \\ x=-2\times3 \\ x=-6 \\ x-\text{intercept of the equation is }(-6,0) \end{gathered}[/tex]Step 4: Find the y-intercept
The y-intercepts are points where the graph of a function or an equation crosses or “touches” the y-axis of the Cartesian Plane. You may think of this as a point with x-value of zero.
To find the y-intercepts of an equation, let x=0 then solve for y
[tex]\begin{gathered} y=-\frac{7}{3}x-14 \\ \text{set x as 0} \\ y=-\frac{7}{3}(0)-14 \\ y=0-14 \\ y=-14 \\ y-\text{intercept of the equation is (0,-14)} \end{gathered}[/tex]Hence, the intercepts of the equations are:
x-intercept=(-6,0)
y-intercept=(0,-14)
