Answer:
Solve for y
.
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Subtract 7x
from both sides of the equation.
−4y=−7x+28
Divide each term by −4
and simplify.
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Divide each term in −4y=−7x+28
by −4
.
−4y−4=−7x−4+28−4
Simplify the left side of the equation
by cancelling the common factors.
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Reduce the expression by cancelling the common factors.
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Factor 4
out of 4y
.
−4(y)−4=−7x−4+28−4
Move the negative one from the denominator of y−1
.
−(−1⋅y)=−7x−4+28−4
Simplify the expression.
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Multiply −1
by y
.
−(−1y)=−7x−4+28−4
Rewrite −1y
as −y
.
y=−7x−4+28−4
Simplify each term.
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Move the negative in front of the fraction.
y=7x4+28−4
Simplify −−7x4
.
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Multiply −1
by −1
.
y=1(7x4)+28−4
Multiply 7x4
by 1
.
y=7x4+28−4
Divide 28
by −4
.
y=7x4−7
Use the slope-intercept form to find the slope and y-intercept.
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The slope-intercept form is y=mx+b
, where m is the slope and b
is the y-intercept.
y=mx+b
Find the values of m
and b using the form y=mx+b
.
m=74
b=−7
The slope of the line is the value of m
, and the y-intercept is the value of b
.
Slope: 74
Y-Intercept: −7
Any line can be graphed using two points. Select two x
values, and plug them into the equation to find the corresponding y
values.
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Choose 0
to substitute in for x
to find the ordered pair.
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Replace the variable x
with 0
in the expression.
f(0)=7(0)4−7
Simplify the result.
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Multiply 7
by 0
.
f(0)=04−7
Divide 0
by 4
.
f(0)=0−7
Subtract 7
from 0
.
f(0)=−7
The final answer is −7
.
−7
The first point is (0,−7)
.
(0,−7)
Choose 1
to substitute in for x
to find the ordered pair.
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Replace the variable x
with 1
in the expression.
f(1)=7(1)4−7
Simplify the result.
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Multiply 7
by 1
.
f(1)=74−7
To write −−71
as a fraction with a common denominator, multiply by 44
.
f(1)=74+−71⋅44
Write each expression with a common denominator of 4
, by multiplying each by an appropriate factor of 1
.
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Combine.
f(1)=74+−7⋅41⋅4
Multiply 4
by 1
.
f(1)=74+−7⋅44
Combine the numerators over the common denominator.
f(1)=7−7⋅44
Simplify the numerator.
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Multiply −7
by 4
.
f(1)=7−284
Subtract 28
from 7
.
f(1)=−214
Move the negative in front of the fraction.
f(1)=−214
The final answer is −214
.
−214
The second point is (1,−214)
.
(1,−214)
Create a table of the x
and y
values.
xy0−71−214
Graph the line using the slope and the y-intercept, or the points.
Slope: 74
Y-Intercept: −7
xy0−71−214
Explanation: