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Questionmylab.pearson.com/Student/PlayerHomework.aspx?homeworkld=687273520\&questionld=312flushed=false\&cld=79288398.back=DoAssignments.aspx?view=homework - College Algebra 1314.A10, A11 \& A12 ework: REVIEW FOR FINAL (part 1) - counts as two grades (new links) Question 36, 2.5.51 Part 1 of 2
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through ( −3,4-3,4 ) and parallel to x+4y=7x+4 y=7. a) The equation of the line in slope-intercept form is −x+1-x+1. (Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)

Studdy Solution

STEP 1

1. We need to find the equation of a line passing through the point (−3,4)(-3, 4).
2. The line is parallel to the line given by the equation x+4y=7x + 4y = 7.
3. We need the equation in both slope-intercept form and standard form.

STEP 2

1. Find the slope of the given line.
2. Use the slope to write the equation of the new line in slope-intercept form.
3. Convert the slope-intercept form to standard form.

STEP 3

Find the slope of the given line x+4y=7x + 4y = 7.
First, rewrite the equation in slope-intercept form y=mx+by = mx + b by solving for yy:
4y=−x+7 4y = -x + 7
Divide every term by 4:
y=−14x+74 y = -\frac{1}{4}x + \frac{7}{4}
The slope mm of the given line is −14-\frac{1}{4}.

STEP 4

Use the slope to write the equation of the new line in slope-intercept form.
Since the line we are finding is parallel to the given line, it has the same slope, −14-\frac{1}{4}.
Use the point-slope form of the equation of a line, y−y1=m(x−x1)y - y_1 = m(x - x_1), where m=−14m = -\frac{1}{4} and (x1,y1)=(−3,4)(x_1, y_1) = (-3, 4):
y−4=−14(x+3) y - 4 = -\frac{1}{4}(x + 3)
Simplify to get the slope-intercept form:
y−4=−14x−34 y - 4 = -\frac{1}{4}x - \frac{3}{4}
Add 4 to both sides:
y=−14x+34+4 y = -\frac{1}{4}x + \frac{3}{4} + 4
Convert 4 to a fraction with a denominator of 4:
y=−14x+34+164 y = -\frac{1}{4}x + \frac{3}{4} + \frac{16}{4}
Combine like terms:
y=−14x+194 y = -\frac{1}{4}x + \frac{19}{4}

STEP 5

Convert the slope-intercept form to standard form.
Start with the slope-intercept form:
y=−14x+194 y = -\frac{1}{4}x + \frac{19}{4}
Multiply every term by 4 to eliminate the fractions:
4y=−x+19 4y = -x + 19
Rearrange to get the standard form Ax+By=CAx + By = C:
x+4y=19 x + 4y = 19
The equation of the line in slope-intercept form is:
y=−14x+194 y = -\frac{1}{4}x + \frac{19}{4}
The equation of the line in standard form is:
x+4y=19 x + 4y = 19

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