Question

Find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept. When typing the point (x,y) be sure to include parentheses and a comma between your x and y components. Do not put any spaces between your characters. If a value is not an integer type your answer rounded to the nearest hundredth.4x-3=2ythe x-intercept is Answerthe y-intercept is Answer

Answer 1

The x-intercept is the x value at which the graph intercects the x-axis. This happens when y = 0, so, to find it without graphing, we just need to input y = 0 and solve for x:

$\begin{gathered} 4x-3=2y \\ 4x-3=2\cdot0 \\ 4x-3=0 \\ 4x=3 \\ x=\frac{3}{4}=0.75 \end{gathered}$

So, the x-intercept is at x = 0.75 and y = 0, that is, at point:

$(0.75,0)$

The y-intercept is similar but is the y value at which the graph intercepts the y-axis, that is, when x = 0.

So, we can input x = 0 and solve for y:

$\begin{gathered} 4x-3=2y \\ 4\cdot0-3=2y \\ -3=2y \\ 2y=-3 \\ y=-\frac{3}{2}=-1.5 \end{gathered}$

Thus, the y-intercept is at x = 0 and y = -1.5, that is, at point:

$(0,-1.5)$