Final answer:
First, calculate the slope using the change in y-coordinates over the change in x-coordinates. Then, use the point-slope form with one of the points and the slope to write the linear equation before rearranging it into the slope-intercept form, resulting in the equation y = -5x + 20.
Step-by-step explanation:
The problem at hand involves finding the slope-intercept form of a linear equation that passes through two provided points on the Cartesian plane. To do this, we'll first calculate the slope, which is the change in y-coordinates divided by the change in x-coordinates between the two points. For points (1, 15) and (2, 10), the slope m is given by (10 - 15) / (2 - 1), which equals -5. Next, we use one of the points (let's use (1, 15)) and the slope to write the equation in point-slope form, y - y1 = m(x - x1). Substituting the values, we get y - 15 = -5(x - 1). Finally, we convert this to slope-intercept form, y = mx + b, by distributing the slope on the right and adding 15 to both sides to isolate y: y = -5x + 20. Therefore, the correct slope-intercept form of the linear equation is y = -5x + 20.