Download Activity 4.5.4 More Standard Form

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More Standard Form
I can find the x-intercept by:
I can find the y-intercept by:
1. Graph the linear functions in standard form by finding the x and y intercepts. Then find the
slope and write the equation in slope-intercept form.
a. Given 3x + 2y = 12, find both intercepts and the slope. Then draw the graph.
x
0
y
y
0
x
x-intercept:
y-intercept:
Slope:
b. Write 3x + 2y = 12 in slope-intercept form: y = mx + b.
c. From the slope-intercept form of the equation, the slope is _____ and the y-intercept is
_______. Check to see that the results agree with your answers in part (a).
Activity 4.5.4
CT Algebra I Model Curriculum Version 3.0
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d. Given 4x – 5y = 20, find both intercepts and the slope. Then draw the graph.
x
0
y
y
0
x
x-intercept:
y-intercept:
Slope:
e. Write 4x – 5y = 20 in slope-intercept form: y = mx + b.
f. From the slope-intercept form of the equation, the slope is _____ and the y-intercept is
_______. Check to see that the results agree with your answers in part (d).
g. Given 6x – 5y = 30, find both intercepts and the slope. Then draw the graph.
x
0
y
y
0
x-intercept:
x
y-intercept:
Slope:
h. Write 6x – 5y = 30 in slope-intercept form: y = mx + b.
Activity 4.5.4
CT Algebra I Model Curriculum Version 3.0
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2. What is one advantage of the standard form (compared to slope-intercept form)?
3. What is one advantage of slope-intercept form?
The standard form of a line is Ax + By = C.
The x’s and y’s are on the same side of the equal sign.
The constant term is alone on the other side of the equal sign.
To find the x-intercept, substitute 0 in for y, and solve for x.
To find the y-intercept, substitute 0 in for x and solve for y.
To transform an equation from standard form to slope-intercept form, solve for y.
The slope-intercept form of a line is y = mx + b.
1. Determine if the equation is in standard form. If not, explain why.
a. 5𝑥 − 𝑦 = 8
d.
𝑥 + 3𝑦 = 0
b. 𝑦 = −4𝑥 − 3
e. 𝑦 = 4 + 4(𝑥 − 2)
c. 𝑥 + 3𝑦 + 7 = −2
f. −6𝑥 + 4𝑦 = −7
2. Find the x-intercept and y-intercept.
a. 5𝑥 + 2𝑦 = 10
c. −4𝑥 + 𝑦 = 4
b. 𝑥 − 3𝑦 = −6
d. 2𝑥 + 4𝑦 = 12
Activity 4.5.4
CT Algebra I Model Curriculum Version 3.0
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3. Plot the intercepts from question 2 and connect them to make a line.
a. 5𝑥 + 2𝑦 = 10
c. −4𝑥 + 𝑦 = 4
y
y
x
b. 𝑥 − 3𝑦 = −6
x
d. 2𝑥 + 4𝑦 = 12
y
y
x
x
4. Use the graphs in question 3 to find the slope of each line.
a. 5𝑥 + 2𝑦 = 10
Slope =
c. −4𝑥 + 𝑦 = 4
Slope =
b. 𝑥 − 3𝑦 = −6
Slope =
d. 2𝑥 + 4𝑦 = 12
Slope =
5. Transform the following equations into slope-intercept form.
a. 5𝑥 + 2𝑦 = 10
c. −4𝑥 + 𝑦 = 4
b. 𝑥 − 3𝑦 = −6
d. 2𝑥 + 4𝑦 = 12
Activity 4.5.4
CT Algebra I Model Curriculum Version 3.0