Questions: Write the slope-intercept form of the equation of the line through the given point with the given slope. 7) through: (1,2), slope = -2 A) y = -5 x + 4 B) y = -2 x + 4 8) through: (1,-2), slope = undefined A) x = -1 B) y = x C) y = -1 D) x = 1

Solution Steps

To write the slope-intercept form of the equation of a line, we can use the point-slope form of a linear equation: $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the given point and $m$ is the slope.

1. For the point $(1,2)$ and slope $-2$:

• Substitute $x_1 = 1$, $y_1 = 2$, and $m = -2$ into the point-slope form.
• Simplify the equation to get it in slope-intercept form $y = mx + b$.

2. For the point $(1,-2)$ and undefined slope:

• An undefined slope means the line is vertical, so the equation will be of the form $x = a$.
• Substitute $x_1 = 1$ into the equation.

The equation of the line passing through the point \((1,2)\) with a slope of \(-2\) is given by \(y = -2x + 4\).

For the line with an undefined slope passing through the point \((1,-2)\), the equation is \(x = 1\).

Final Answer