Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = - 3/5, passing through (10, −4)

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Recall the point-slope form of a line equation: \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a point on the line.

Substitute the given slope \(m = -\frac{3}{5}\) and the point \((10, -4)\) into the point-slope form: \(y - (-4) = -\frac{3}{5}(x - 10)\).

Simplify the left side by changing \(y - (-4)\) to \(y + 4\), so the equation becomes \(y + 4 = -\frac{3}{5}(x - 10)\).

To write the equation in slope-intercept form \(y = mx + b\), distribute the slope on the right side: \(y + 4 = -\frac{3}{5}x + \frac{3}{5} \times 10\).

Finally, isolate \(y\) by subtracting 4 from both sides: \(y = -\frac{3}{5}x + \frac{3}{5} \times 10 - 4\).

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주요 개념

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Point-Slope Form of a Line

The point-slope form is an equation of a line expressed as y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. It directly uses the given slope and point to write the line's equation.

Slope-Intercept Form of a Line

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. After finding the equation in point-slope form, you can solve for y to rewrite it in slope-intercept form, identifying the y-intercept.

Slope of a Line

Slope measures the steepness of a line and is the ratio of vertical change to horizontal change between two points. A slope of -3/5 means the line falls 3 units vertically for every 5 units it moves horizontally to the right.