The line represented by the equation intersects the -axis at which point?
For any SAT question asking where a line intersects the y-axis, immediately set in the equation and solve for ; this is faster and less error-prone than fully rewriting the equation. Remember: y-intercept means , x-intercept means . After finding the coordinate, quickly check that it matches both the equation and the requested axis before selecting your answer.
Hints
Think about points on the y-axis
What is always true about the -coordinate of any point that lies on the y-axis?
Use the equation of the line
Once you know the value of for points on the y-axis, substitute that value of into the equation .
Solve the resulting equation
After substituting for , you should have an equation with only . Solve that equation, then write the point as .
Desmos Guide
Graph the line
In Desmos, type the equation 4y - 8x = 12. Desmos will automatically rearrange and graph the line.
Identify the y-intercept visually
Look at where the graph crosses the y-axis (the vertical axis). Hover your cursor over that intersection point; Desmos will display its coordinates.
Confirm algebraically in Desmos
In another line, type y = (12 + 8x)/4 to see the equivalent slope-intercept form. Then either read the y-intercept from the equation or substitute x = 0 in Desmos to see the corresponding y-value.
Step-by-step Explanation
Interpret what 'intersects the y-axis' means
A point on the y-axis has an -coordinate of . So, to find where the line crosses the y-axis, we need the point on the line where .
Substitute into the equation
Take the line's equation and plug in :
This simplifies to:
Solve for and write the point
Now solve by dividing both sides by :
So when , . The line intersects the y-axis at the point .