Question

Consider a system of two linear equations. The line represented by the first equation has a slope of -(1)/(4) and a y-intercept point of (0,8). The line represented by the second equation passes hrough the points (-2,-1) and (1,5)

Answer 1

The first equation has a slope of -(1)/(4) and y-intercept of (0,8), while the second equation passes through (-2,-1) and (1,5). The equations can be written as y = -(1)/(4)x + 8 and y = 2x + 3 respectively.

Step-by-step explanation:

The first equation has a slope of -(1)/(4) and a y-intercept of (0,8). This means that for every increase of 1 on the horizontal axis, there will be a decrease of 1/4 on the vertical axis. The equation can be written as y = -(1)/(4)x + 8.

The second equation passes through the points (-2,-1) and (1,5). We can use the two-point form of the equation to find the equation. The slope can be calculated as (5-(-1))/(1-(-2)) = 2. Using the point-slope form of the equation, the equation can be written as y - (-1) = 2(x - (-2)) which simplifies to y = 2x + 3.