List the 𝑥-intercept and the 𝑦-intercept of the line two 𝑥 minus three 𝑦 equals seven.
We begin by recalling that the 𝑥- and 𝑦-intercepts are the points at which our line crosses the 𝑥- and 𝑦-axes, respectively. Any straight line, as in this case, will cross the 𝑥-axis when 𝑦 equals zero and cross the 𝑦-axis when 𝑥 equals zero. These points will then have coordinates 𝑎, zero and zero, 𝑏, respectively. Setting 𝑦 equal to zero, our equation becomes two 𝑥 is equal to seven. We can then divide through by two, giving us 𝑥 is equal to seven over two. This means that the point at which this line intercepts the 𝑥-axis is seven over two, zero.
Next, we can set 𝑥 equal to zero, giving us negative three 𝑦 equals seven. Dividing through by negative three, we have 𝑦 is equal to negative seven over three. The point at which the line intercepts the 𝑦-axis is zero, negative seven over three. The 𝑥- and 𝑦-intercepts of the line two 𝑥 minus three 𝑦 equals seven are seven over two, zero and zero, negative seven over three.