Find the equation in slope-intercept form for the line passing through the points with the given coordinates. (−2,−3),(1,4)

Sure, here are the steps to find the equation of the line in slope-intercept form (y = mx + b) that passes through the points (-2,-3) and (1,4).

Step 1: Find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Substitute the given points into the formula: m = (4 - (-3)) / (1 - (-2)) = 7/3.

Step 2: Now that we have the slope, we can use the point-slope form of a line, which is y - y1 = m(x - x1). Substitute one of the given points and the slope into the formula: y - 4 = 7/3 * (x - 1).

Step 3: Simplify the equation to get it into slope-intercept form (y = mx + b). First distribute the 7/3: y - 4 = 7/3x - 7/3. Then add 4 to both sides: y = 7/3x + 5/3.

So, the equation of the line in slope-intercept form that passes through the points (-2,-3) and (1,4) is y = 7/3x + 5/3.