Complete the point-slope equation of the line through (1,0) and (6,-3). Use exact numbers. y-(-3)=◻

Find the Slope: First, find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the given points. So, m = (-3 - 0) / (6 - 1) = -3 / 5.Use Point-Slope Form: Now, use the point-slope form y - y1 = m(x - x1) with one of the points and the slope we found. Let's use the point (6, -3) and the slope -3/5. So, y - (-3) = (-3/5)(x - 6).Simplify Equation: Simplify the equation by distributing the slope on the right side. y + 3 = (-3/5)x + (3/5)*6.Combine Constant Terms: Now, simplify the constant term on the right side. y + 3 = (-3/5)x + 18/5.Subtract 3: Subtract 3 from both sides to get the final point-slope form. y = (-3/5)x + 18/5 - 3.Convert 3 to Fraction: Convert 3 to a fraction with a denominator of 5 to combine like terms. y = (-3/5)x + 18/5 - 15/5.Combine Constant Terms: Combine the constant terms on the right side. y = (-3/5)x + 3/5.

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Math Problems

Grade 8

Write a linear equation from two points

Full solution

Q. Complete the point-slope equation of the line through

(1,0)

and

(6,-3)

\newline

Use exact numbers.

\newline

y-(-3)=\square

Find the Slope: First, find the slope $m$ of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are the given points. $\newline$ So, $m = \frac{-3 - 0}{6 - 1} = \frac{-3}{5}$ .
Use Point-Slope Form: Now, use the point-slope form $y - y_1 = m(x - x_1)$ with one of the points and the slope we found. $\newline$ Let's use the point $(6, -3)$ and the slope $-\frac{3}{5}$ . $\newline$ So, $y - (-3) = (-\frac{3}{5})(x - 6)$ .
Simplify Equation: Simplify the equation by distributing the slope on the right side. $y + 3 = \left(-\frac{3}{5}\right)x + \left(\frac{3}{5}\right)\cdot 6$ .
Combine Constant Terms: Now, simplify the constant term on the right side. $\newline$ $y + 3 = \left(-\frac{3}{5}\right)x + \frac{18}{5}$ .
Subtract $3$ : Subtract $3$ from both sides to get the final point-slope form. $\newline$ $y = \left(-\frac{3}{5}\right)x + \frac{18}{5} - 3$ .
Convert $3$ to Fraction: Convert $3$ to a fraction with a denominator of $5$ to combine like terms. $\newline$ $y = \left(-\frac{3}{5}\right)x + \frac{18}{5} - \frac{15}{5}.$
Combine Constant Terms: Combine the constant terms on the right side. $\newline$ $y = \left(-\frac{3}{5}\right)x + \frac{3}{5}$ .