Algebra 1: Point-Slope Form and Slope-Intercept Form

Practice flashcards covering linear equations in Point-Slope Form (Lesson 2.2) and Slope-Intercept Form (Lesson 2.1), including key definitions, graphing steps, and practice problems.

What is the general equation formula for point-slope form?

$$y - y_1 = m(x - x_1)$$

In the point-slope form equation $y - y_1 = m(x - x_1)$, what do $m$ and $(x_1, y_1)$ represent?

$m$ represents the slope of the line, and $(x_1, y_1)$ represents a point on the line.

What are the four steps for graphing a line using point-slope form?

1. Identify the point and slope from the equation. 2. Plot the point on the graph. 3. Use the slope to find more points. 4. Sketch a line through the graph.

What are the slope and point identified from the equation $y - 2 = \frac{1}{3}(x - 3)$?

Slope = $\frac{1}{3}$ and Point = $(3, 2)$

What are the slope and point identified from the equation $y - 5 = 2(x + 8)$?

Slope = $2$ and Point = $(-8, 5)$

What are the slope and point identified from the equation $y + 6 = -5(x + 4)$?

Slope = $-5$ and Point = $(-4, -6)$

What is the equation in point-slope form for a line passing through $(1, -5)$ with a slope of $m = -3$?

$$y + 5 = -3(x - 1)$$

What is the equation in point-slope form for a line passing through $(3, -2)$ with a slope of $m = -\frac{1}{2}$?

$$y + 2 = -\frac{1}{2}(x - 3)$$

Given the two points $(-1, -7)$ and $(2, -4)$, what is the slope $m$ and the point-slope form equation using the first point?

Slope $m = 1$ and equation $y + 7 = 1(x + 1)$

Given the two points $(-4, -2)$ and $(1, 6)$, what is the slope $m$ and the point-slope form equation using the first point?

Slope $m = \frac{8}{5}$ and equation $y + 2 = \frac{8}{5}(x + 4)$

What is the general formula for linear equations in slope-intercept form?

$$y = mx + b$$

In slope-intercept form $y = mx + b$, what do $m$ and $b$ represent?

$m$ represents the slope ($\frac{\Delta y}{\Delta x}$) and $b$ represents the y-intercept $(0, y)$.

How is the y-intercept defined in Lesson 2.1?

A point where the line crosses the y-axis, represented as $(0, y)$.

What is the slope-intercept equation for a line with slope $m = -\frac{3}{4}$ and y-intercept $(0, 1)$?

$$y = -\frac{3}{4}x + 1$$

What are the slope and y-intercept of the linear equation $y = -3x + 8$?

Slope = $-3$ (or $\frac{-3}{1}$) and y-intercept = $8$ (or $(0, 8)$).

What are the four steps to write a linear equation in slope-intercept form when given two points?

1. Find the slope by finding the difference in y-values and dividing it by the difference in x-values. 2. Plug in the slope AND one of the points to find the y-intercept or $b$. 3. Solve for $b$. 4. Plug $m$ and $b$ into $y = mx + b$.

What is the slope-intercept equation for the line containing the points $(2, 4)$ and $(4, 8)$?

$$y = 2x + 0$$

What is the slope-intercept equation for the line containing the points $(-3, 0)$ and $(6, -15)$?

$$y = -\frac{5}{3}x - 5$$

What is the slope-intercept equation for the line containing the points $(4, 8)$ and $(0, 16)$?

$$y = -2x + 16$$

What is the slope-intercept equation for the line containing the points $(-3, 0)$ and $(-9, 12)$?

$$y = -2x - 6$$