Three linear equations in slope-intercept form that pass through (-2, 5) could be y = 2x + 9, y = -x + 3, and y = 0.5x + 6. Their slopes are chosen arbitrarily and demonstrate how the specified point affects the y-intercept of each line.
To write 3 linear equations in slope-intercept form that all pass through the point (-2, 5), we use the general format y = mx + b, where m is the slope and b is the y-intercept. The main answer in 2 lines is that any line with the slope m and passing through (-2, 5) can be given by plugging in the coordinates into y - y1 = m(x - x1) to find the y-intercept b and then rewriting as y = mx + b.
Choose different slopes (for example 2, -1, 0.5). Using one of these slopes, say 2, we will find the y-intercept by using the point-slope formula: 5 - 2(-2) = 5 + 4 = 9, so one line is y = 2x + 9. Similarly, for a slope of -1, the equation becomes 5 - (-1)(-2) = 5 - 2 = 3, leading to the line y = -x + 3. Lastly, using 0.5 as the slope, the y-intercept is calculated as 5 - 0.5(-2) = 5 + 1 = 6, resulting in y = 0.5x + 6.
these equations represent different lines that all intersect at the point (-2, 5), demonstrating how the slope influences the steepness and direction of the line, while the y-intercept determines where it crosses the y-axis.