Find an equation of the line that passes through the points (−3,5) and (1,2)Give your answer in the form 𝑎𝑥+𝑏𝑦=𝑐 where 𝑎, 𝑏 and 𝑐 are integers.

Step 1: Find the slope of the line. The formula for the slope (m) is (y2 - y1) / (x2 - x1).

Substitute the given points into the formula: m = (2 - 5) / (1 - (-3)) = -3 / 4 = -0.75

Step 2: Use the point-slope form of a line, which is y - y1 = m(x - x1).

Substitute the slope and one of the points into the formula: y - 5 = -0.75(x - (-3))

Step 3: Simplify the equation.

y - 5 = -0.75x - 2.25

Step 4: Convert the equation into the standard form ax + by = c.

0.75x + y = 7.25

Step 5: To get the equation in the form where a, b, and c are integers, multiply the entire equation by 4 (the denominator of the slope).

3x + 4y = 29

So, the equation of the line that passes through the points (-3,5) and (1,2) is 3x + 4y = 29.

Step 1: Find the slope of the line. The formula for the slope (m) is (y2 - y1) / (x2 - x1).

Substitute the given points into the formula: m = (2 - 5) / (1 - (-3)) = -3 / 4 = -0.75

Step 2: Use the point-slope form of a line equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Substitute the slope and one of the points into the equation: y - 5 = -0.75(x - (-3))

Step 3: Simplify the equation and convert it to the standard form ax + by = c.

y - 5 = -0.75x - 2.25 0.75x + y = 7.25

Step 4: To get the equation in the form where a, b, and c are integers, multiply the entire equation by 4 (the denominator of the fraction 0.75).

3x + 4y = 29

So, the equation of the line that passes through the points (-3,5) and (1,2) is 3x + 4y = 29.