Select the two statements that are true about the equation y + 6 = -10(x – 3).
The slope of the line is -10.
The slope of the line is 3.
One point on the line is (3, 6).
One point on the line is (3, -6).
Select the two statements that are true about the equation y + 6 = -10(x – 3)
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To determine which statements are true about the equation ( y + 6 = -10(x – 3) ), we first need to rewrite it in the slope-intercept form ( y = mx + b ), where ( m ) is the slope.
1. Start with the given equation:
[ y + 6 = -10(x – 3) ]
2. Distribute -10 on the right side:
[ y + 6 = -10x + 30 ]
3. Now, subtract 6 from both sides to solve for ( y ):
[ y = -10x + 30 – 6 ]
[ y = -10x + 24 ]
From this, we can see that the slope ( m ) is -10.
Next, let’s substitute ( x = 3 ) into the equation to find the corresponding ( y )-value:
[ y = -10(3) + 24 ]
[ y = -30 + 24 ]
[ y = -6 ]
This means one point on the line is (3, -6).
Now, let’s evaluate the statements:
– The slope of the line is -10. (True)
– The slope of the line is 3. (False)
– One point on the line is (3, 6). (False)
– One point on the line is (3