Question

p) determine the equation of the line in y = ax + c form that has:

• a slope of -2
• passes through the point (4,10)

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Here, the equation is in the form \(y=ax + c\), so \(a\) is the slope and \(c\) is the y - intercept. We know that the slope \(a=- 2\), so the equation becomes \(y=-2x + c\).

Step2: Substitute the point into the equation

We know that the line passes through the point \((x,y)=(4,10)\). Substitute \(x = 4\), \(y = 10\) and \(a=-2\) into the equation \(y=ax + c\).

$$10=-2\times4 + c$$

Step3: Solve for \(c\)

First, calculate \(-2\times4=-8\). Then the equation becomes \(10=-8 + c\). Add 8 to both sides of the equation: \(c=10 + 8=18\).

Step4: Write the final equation

Now that we know \(a=-2\) and \(c = 18\), the equation of the line in the form \(y=ax + c\) is \(y=-2x+18\).

Answer:

The equation of the line is \(y=-2x + 18\)