The image shows eight linear equations, each given in
general form and then converted to
slope-intercept form. Since no specific question was asked (like “verify these” or “convert one of them”), but the user says “solve the problem accurately,” I will assume the task is to
verify that each slope-intercept form correctly matches its general form.
I’ll go through each pair step by step, converting the general form to slope-intercept form myself, and check if it matches what’s shown.
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a) General: \( x + 3y - 5 = 0 \)
Solve for y:
\( 3y = -x + 5 \)
\( y = -\frac{1}{3}x + \frac{5}{3} \) →
✔ Matches given slope-int.
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b) General: \( 3x + 4y + 6 = 0 \)
\( 4y = -3x - 6 \)
\( y = -\frac{3}{4}x - \frac{6}{4} = -\frac{3}{4}x - \frac{3}{2} \) →
✔ Matches.
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c) General: \( x - 2y + 10 = 0 \)
\( -2y = -x - 10 \)
Multiply both sides by -1: \( 2y = x + 10 \)
\( y = \frac{1}{2}x + 5 \) →
✔ Matches.
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d) General: \( 3x - y - 4 = 0 \)
\( -y = -3x + 4 \)
Multiply by -1: \( y = 3x - 4 \) →
✔ Matches.
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e) General: \( 2x + y + 5 = 0 \)
\( y = -2x - 5 \) →
✔ Matches.
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f) General: \( 3x + y - 17 = 0 \)
\( y = -3x + 17 \) →
✔ Matches.
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g) General: \( x + y + \sqrt{2} - 6 = 0 \)
Rewrite as: \( x + y + (\sqrt{2} - 6) = 0 \)
Then: \( y = -x - (\sqrt{2} - 6) = -x + 6 - \sqrt{2} \) →
✔ Matches.
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h) General: \( x + 12y - 12 = 0 \)
\( 12y = -x + 12 \)
\( y = -\frac{1}{12}x + 1 \) →
✔ Matches.
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✔ All conversions are correct.
Final Answer:
All given slope-intercept forms correctly match their respective general forms.
Parent Tip: Review the logic above to help your child master the concept of analytic geometry worksheet.
