Given the equation for line z as y = -2x + 3 and the fact that line r passes through the point (1,4), let’s use the point-slope formula to find the equation of line r:
Point-Slope Form: y - y₁ = m(x - x₁)
Where (x₁, y₁) is the point (1,4), and m is the slope of line r.
The slope of line r will be the same as the slope of line z because they pass through the same spot on the y-axis. The slope of line z is -2.
Now, plug in the values into the point-slope formula:
y - 4 = -2(x - 1)
Simplify the equation:
y - 4 = -2x + 2
Now, isolate y:
y = -2x + 6