About Slope Intercept Form:
When we work with the equation of a line, we use different forms based on the situation. The slope-intercept form: y = mx + b is used when we want to know the slope (m) and y-intercept (b). Additionally, we have the point-slope form: y - y1 = m(x - x1) which can be used when we know the point and the slope or two points. Lastly, we have standard form: ax + by = c, where a, b, and c are integers, a ≥ 0, and the greatest common factor (gcf) of a, b, and c is 1.
Test Objectives
- Demonstrate the ability to write the equation of a line in standard form
- Demonstrate the ability to write the equation of a line in slope-intercept form
- Demonstrate the ability to write the equation of a line in point-slope form
#1:
Instructions: Write the slope-intercept form of the equation of each line, given the slope and y-intercept.
a) $$\text{y-int:} \, {-}2, m = -\frac{2}{5}$$
b) $$\text{y-int:} \, 1, m = \frac{3}{4}$$
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#2:
Instructions: Write the slope-intercept form of the equation of each line, given the slope and y-intercept.
a) $$\text{y-int:} \, 3, m = -\frac{5}{4}$$
b) $$\text{y-int:} \, 5, m = -6$$
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#3:
Instructions: Graph each line.
a) $$y = -2x + 4$$
b) $$y = \frac{4}{5}x + 1$$
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#4:
Instructions: Write each equation using point-slope form, then solve for y and place the equation in slope-intercept form.
a) through (-5, 3) : m = 2
b) through (-1, 2) : m = -3
c) through (0, -5) and (5, 2)
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#5:
Instructions: Write the standard form of the equation of the line.
a) $$y = -\frac{7}{3}x + 1$$
b) $$y = \frac{1}{5}x + 3$$
c) $$y = -\frac{9}{5}x + 6$$
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Written Solutions:
#1:
Solutions:
a) $$y = -\frac{2}{5}x - 2$$
b) $$y = \frac{3}{4}x + 1$$
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#2:
Solutions:
a) $$y = -\frac{5}{4}x + 3$$
b) $$y = -6x + 5$$
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#3:
Solutions:
a) $$y = -2x + 4$$
b) $$y = \frac{4}{5}x + 1$$
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#4:
Solutions:
a) point-slope form:$$y - 3 = 2(x - (-5))$$ slope-intercept form: $$y = 2x + 13$$
b) point-slope form:$$y - 2 = -3(x - (-1))$$ slope-intercept form: $$y = -3x - 1$$
c) point-slope form: $$y - 2 = \frac{7}{5}(x - 5)$$ slope-intercept form: $$y = \frac{7}{5}x - 5$$
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#5:
Solutions:
a) $$7x + 3y = 3$$
b) $$x - 5y = -15$$
c) $$9x + 5y = 30$$
