Question

Ind the xx and yy intercepts of the equation: −7x−3y=42-7x-3y=42 The intercepts are

Answer 1

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

`-7x-3y=42`

Step 2: Write the equation in form of a slope-intercept form by making y the subject of the formula

`\begin{gathered} -7x-3y=42 \\ -3y=42+7x \\ \text{divide both sides by -3} \\ y=-(42+7x)/(3) \\ y=-((42)/(3)+(7x)/(3)) \\ y=-(14+(7x)/(3)) \\ y=-(7)/(3)x-14 \end{gathered}`

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

`\begin{gathered} y=-(7)/(3)x-14 \\ \text{set y=0} \\ 0=-(7)/(3)x-14 \\ (7)/(3)x=-14 \\ \text{multiply both sides by inverse of 7/3} \\ (7)/(3)x*(3)/(7)=-14*(3)/(7) \\ x=-2*3 \\ x=-6 \\ x-\text{intercept of the equation is }(-6,0) \end{gathered}`

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

`\begin{gathered} y=-(7)/(3)x-14 \\ \text{set x as 0} \\ y=-(7)/(3)(0)-14 \\ y=0-14 \\ y=-14 \\ y-\text{intercept of the equation is (0,-14)} \end{gathered}`

Hence, the intercepts of the equations are:

x-intercept=(-6,0)

y-intercept=(0,-14)