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Point-Slope Form and Equations of Lines Example 1: Find the equation of a line in standard form that passes through point A(4,-5) and has slope -(1)/(4) What is your strotegy?

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Point-Slope Form and Equations of Lines Example 1: Find the equation of a line in standard form that passes through point A(4,-5) and has slope -(1)/(4) What is your strotegy?

Point-Slope Form and Equations of Lines
Example 1: Find the equation of a line in standard form that passes through point A(4,-5) and has slope -(1)/(4)
What is your strotegy?

Solution

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LailaVeteran · Tutor for 12 years

Answer

### $x + 4y = -16$

Explain

## Step 1: Point-Slope Form<br />### We start by plugging the given point $(x_1, y_1) = (4, -5)$ and slope $m = -\frac{1}{4}$ into the point-slope form equation: $y - y_1 = m(x - x_1)$. This gives us $y - (-5) = -\frac{1}{4}(x - 4)$, which simplifies to $y + 5 = -\frac{1}{4}(x - 4)$.<br /><br />## Step 2: Simplify the Equation<br />### Distribute the $-\frac{1}{4}$ on the right side: $y + 5 = -\frac{1}{4}x + 1$.<br /><br />## Step 3: Convert to Standard Form<br />### Standard form is $Ax + By = C$, where $A$, $B$, and $C$ are integers, and $A$ is non-negative. Add $\frac{1}{4}x$ to both sides: $\frac{1}{4}x + y + 5 = 1$. Subtract 5 from both sides: $\frac{1}{4}x + y = -4$. Multiply the entire equation by 4 to eliminate the fraction: $x + 4y = -16$.
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